论文标题
内核PCA的分散框架，具有投影共识约束
A Decentralized Framework for Kernel PCA with Projection Consensus Constraints
论文作者
论文摘要
本文在分散的环境中研究了内核PCA，其中禁止在局部节点中分布数据，并禁止在局部节点和融合中心观察到数据。与线性PCA相比，内核的使用给分散的共识优化的设计带来了挑战：局部投影方向是数据依赖性的。结果，分布式线性PCA的共识约束不再有效。为了克服这个问题，我们提出了一个投影共识约束，并获得有效的分散共识框架，在该框架中，本地解决方案被期望为在本地数据集的列空间上的全局解决方案的投影。我们还基于乘数的替代方向方法得出了一种完全非参数，快速和收敛算法，其中每种迭代都是分析性和沟通效率的。在现实世界数据上进行了真正并行结构的实验，表明所提出的分散算法有效地利用了其他节点的信息，并且在中央内核PCA上运行时间具有很大的优势。
This paper studies kernel PCA in a decentralized setting, where data are distributively observed with full features in local nodes and a fusion center is prohibited. Compared with linear PCA, the use of kernel brings challenges to the design of decentralized consensus optimization: the local projection directions are data-dependent. As a result, the consensus constraint in distributed linear PCA is no longer valid. To overcome this problem, we propose a projection consensus constraint and obtain an effective decentralized consensus framework, where local solutions are expected to be the projection of the global solution on the column space of local dataset. We also derive a fully non-parametric, fast and convergent algorithm based on alternative direction method of multiplier, of which each iteration is analytic and communication-effcient. Experiments on a truly parallel architecture are conducted on real-world data, showing that the proposed decentralized algorithm is effective to utilize information of other nodes and takes great advantages in running time over the central kernel PCA.
